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3 years ago

Solve for x: log(3x) + log(x + 4) = log(15).

Mathematics

2 answers:

Eduardwww [97]3 years ago

7 0

Answer:

x=1

Step-by-step explanation:

The given equation is

$\log(3x)+\log (x+4)=\log (15)$

We need to solve the equation for x.

Using the product property of logarithm we get

$\log(3x(x+4))=\log (15)$ $[\because \log (ab)=\log a+\log b]$

$\log(3x^2+12x)=\log (15)$

On comparing both sides we get

$3x^2+12x=15$

$3x^2+12x-15=0$

Find factors using grouping method.

$3x^2+15x-3x-15=0$

$3x(x+5)-3(x+5)=0$

$(x+5)(3x-3)=0$

Using zero product property we get

$x+5=0\Rightarrow x=-5$

$3x-3=0\Rightarrow x=1$

For x=-5, 3x=-15 and log is not defined for negative values.

It means x=-5 is an extraneous solution.

Therefore, x=1 is the only valid solution of the given equation.

Fed [463]3 years ago

6 0

Answer:

The solutions are x = 1 and x = -5

Step-by-step explanation:

Hi there!

First, let´s write the equation:

log(3x) + log(x + 4) = log(15)

Apply logarithm property: log(3x) = log(3) + log(x)

log(3) + log(x) + log(x + 4) = log(15)

Substract log(3) from both sides of the equation

log(x) + log(x+4) = log(15) - log(3)

Apply logarithm property: log(15) - log(3) = log(15/3) = log(5)

log(x) + log(x + 4) = log(5)

Apply logarithm property: log(x) + log(x+4) = log(x (x+4)) = log(x² + 4x)

log(x² + 4x) = log(5)

Apply logarithm equality rule: if log(x² + 4x) = log(5), then x² + 4x = 5

x² + 4x = 5

Substract 5 from both sides

x² + 4x - 5 = 0

Using the quadratic formula (a = 1, b = 4, c = -5)

x = 1 and x = -5

The solutions are x = 1 and x = -5

Have a nice day!

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How do i solve functions?

Maksim231197 [3]

Most quadratic functions(which is what you have there, to a degree of 2) are solved using factoring and the zero product law. If you can not factor then you have to use the quadratic formula or graph it. However this one can be factored.
It's pretty simple to just factor it by inspection but I use the chart method, if you know decomposition that works as well.
Factoring gives us,
$(2x + 1)(x - 3) = 0$
Then you set each factor to 0 and solve for x,
$2x + 1 = 0$
$2x = - 1$
$x = \frac{ - 1}{2}$
And the second one,
$x - 3 = 0$
$x = 3$
The solutions to this equation are
x = -1/2, 3

6 0

3 years ago

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first deter

JulsSmile [24]

Answer:

1) n=114

2) n=59

3) On this case no, because if we survey just the adults of the nearest college that would be a convenience sample. And when we use "convenience sample" we have some problems associated to bias. This methodology it's not appropiate in order to have a good estimation of the parameter of interest. It's better use a random, cluster or stratified sampling.

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 80% of confidence, our significance level would be given by $\alpha=1-0.80=0.2$ and $\alpha/2 =0.1$ . And the critical value would be given by:

$z_{\alpha/2}=-1.28, z_{1-\alpha/2}=1.28$

Part 1

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.06$ or 6% points, and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Since we don't have a prior estimate of $\het p$ we can use 0.5 as a good estimate, replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.06}{1.28})^2}=113.77$

And rounded up we have that n=114

Part 2

On this case we have a prior estimate for the population proportion and is $\hat p =0.85$ so replacing the values into equation (b) we got:

$n=\frac{0.85(1-0.85)}{(\frac{0.06}{1.28})^2}=58.027$

And rounded up we have that n=59

Part 3

On this case no, because if we survey just the adults of the nearest college that would be a convenience sample. And when we use "convenience sample" we have some problems associated to bias. This methodology it's not appropiate in order to have a good estimation of the parameter of interest. It's better use a random, cluster or stratified sampling.

5 0

3 years ago

PLEASE HELP WILL GIVE BRAINLIEST AND MY NUMBER

m_a_m_a [10]

I think it’s 3 and 2/6! sorry if im wrong but i hope this helps

4 0

2 years ago

Read 2 more answers

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hammer [34]

Answer:

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Step-by-step explanation:

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3 years ago

Explain how you would graph 3x+9y= -18 without converting to slope-intercept form

Zolol [24]

Answer:

you would solve using x and y intercepts.

Step-by-step explanation:

for the X intercept, Y=0

3x=-18. you divide by three on both sides

x=-6. (-6,0)

the for the y intercept, X=0

+9y=-18. you divide 9 on both sides.

y=-2. (0,-2)

then you graph both and connect the points on the x and y axis.

Brainiest always accepted!!!!1

8 0

3 years ago